Finite Group Databasebeta

← #16945445

Subgroups — #16945445

Order 4352.

452 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14534138C211yesmaximal, characteristic
2#14528772C211yesmaximal, characteristic
3#14526809C212yesmaximal, complemented
4#14526806C212yesmaximal, complemented
5C17×#1459C211yesmaximal, characteristic
6C2×C4×Dic34C411yescharacteristic, complemented
7C2×#10587505—21no—
8#11762745C411yescharacteristic, complemented
9#11762745C2211yescharacteristic
10#11762721C411yescharacteristic, complemented
11#11762721C2211yescharacteristic
12#11762712—21no—
13#11762705—21no—
14#11762682—21no—
15#11762682—21no—
16#11762675C411yescharacteristic, complemented
17#11762669—21no—
18#11762576C2212yes—
19C2×C4×D4×C17C2211yescharacteristic
20C2×C17×C22⋊C8—21no—
21C17×#324—21no—
22C17×#323C2212yes—
23C22×D4×C17D411yescharacteristic
24C23×C4×C17D411yescharacteristic
25C23×C4×C17D411yescharacteristic
26C22×Dic34C2×C411yescharacteristic
27C22×C8×C17—41no—
28C4×D4×C17—41no—
29C4×D4×C17—41no—
30C2×C4⋊C4×C17D411yescharacteristic
31C2×C22⋊C4×C17C2×C411yescharacteristic
32C2×C22⋊C4×C17C2311yescharacteristic
33C2×C42×C17C2×C411yescharacteristic
34C2×C22⋊Dic17—21no—
35C2×C22⋊Dic17—21no—
36C2×C22⋊Dic17—22no—
37C2×C22⋊Dic17—21no—
38C2×C22⋊Dic17—21no—
39C2×C4⋊Dic17—21no—
40C2×C4⋊Dic17—41no—
41C2×C4⋊Dic17C2×C411yescharacteristic
42C2×#63225—21no—
43C2×#63225—21no—
44C2×#63225—21no—
45C2×C4×Dic17—21no—
46C4×Dic34—41no—
47C4×Dic34—41no—
48C17×C22⋊C8—22no—
49C17×C22⋊C8—41no—
50#10587505—42no—
51#10587502—21no—
52#10587502—21no—
53#10587502—21no—
54#10587502—41no—
55#10587502C2×C411yescharacteristic
56#10587502C2×C411yescharacteristic
57C24×C17C22⋊C411yescharacteristic
58C24×C17C2×D411yescharacteristic
59C2×D4×C17—41no—
60C2×D4×C17—41no—
61C2×D4×C17SD1612yes—
62C2×D4×C17Q1612yes—
63C22×C4×C17—21no—
64C22×C4×C17—21no—
65C22×C4×C17—21no—
66C22×C4×C17—21no—
67C22×C4×C17—81no—
68C22×C4×C17—81no—
69C22×C4×C17C22⋊C411yescharacteristic
70C22×C4×C17C22⋊C411yescharacteristic
71C22×C4×C17C22⋊C411yescharacteristic
72C22×C4×C17C22×C411yescharacteristic
73C22×C4×C17C2×D411yescharacteristic
74C22×Dic17—21no—
75C22×Dic17—21no—
76C22×Dic17—21no—
77C22×Dic17—21no—
78C22×Dic17—42no—
79C2×Dic34—41no—
80C2×Dic34—42no—
81C2×C8×C17—42no—
82C2×C8×C17—82no—
83C4⋊C4×C17—41no—
84C22⋊C4×C17—41no—
85C22⋊C4×C17—41no—
86C42×C17—21no—
87C42×C17—21no—
88C22⋊Dic17—42no—
89C22⋊Dic17—42no—
90C22⋊Dic17—42no—
91C22⋊Dic17—42no—
92C22⋊Dic17—81no—
93C22⋊Dic17—81no—
94C4⋊Dic17—42no—
95C4⋊Dic17—41no—
96C4⋊Dic17—82no—
97#63225—41no—
98#63225—41no—
99#63225—81no—
100#63225—81no—
101C4×Dic17—42no—
102#11897—171nomaximal, Sylow
103C23×C17—21no—
104C23×C17—21no—
105C23×C17—21no—
106C23×C17—21no—
107C23×C17—41no—
108C23×C17—41no—
109C23×C17—41no—
110C23×C17—41no—
111C23×C17#10312yes—
112C23×C17C2×C22⋊C411yescharacteristic
113C23×C17C2×SD1611yescharacteristic
114C23×C17C2×Q1611yescharacteristic
115D4×C17—42no—
116D4×C17—42no—
117C2×C4×C17—21no—
118C2×C4×C17—21no—
119C2×C4×C17—21no—
120C2×C4×C17—21no—
121C2×C4×C17—21no—
122C2×C4×C17—41no—
123C2×C4×C17—42no—
124C2×C4×C17—42no—
125C2×C4×C17—41no—
126C2×C4×C17—41no—
127C2×C4×C17—41no—
128C2×C4×C17—81no—
129C2×C4×C17—81no—
130C2×C4×C17#9911yescharacteristic
131C2×C4×C17#9911yescharacteristic
132C2×C4×C17#10312yes—
133C2×Dic17—22no—
134C2×Dic17—41no—
135C2×Dic17—41no—
136C2×Dic17—41no—
137C2×Dic17—41no—
138C2×Dic17—41no—
139C2×Dic17—41no—
140C2×Dic17—41no—
141C2×Dic17—41no—
142C2×Dic17—41no—
143C2×Dic17—41no—
144C2×Dic17—41no—
145C2×Dic17—82no—
146C2×Dic17—82no—
147C2×Dic17—82no—
148Dic34—42no—
149Dic34—42no—
150C8×C17—82no—
151#2580—171no—
152#1799—171no—
153#1459D1711yescharacteristic
154#1352—172no—
155#1351—172no—
156C22×C17—21no—
157C22×C17—21no—
158C22×C17—21no—
159C22×C17—22no—
160C22×C17—21no—
161C22×C17—42no—
162C22×C17—41no—
163C22×C17—41no—
164C22×C17—41no—
165C22×C17—41no—
166C22×C17—41no—
167C22×C17—41no—
168C22×C17—81no—
169C22×C17—81no—
170C22×C17C2×#9911yescharacteristic
171C22×C17C2×#10311yescharacteristic
172C22×C17#42111yescharacteristic
173C4×C17—21no—
174C4×C17—21no—
175C4×C17—22no—
176C4×C17—41no—
177C4×C17—41no—
178C4×C17—41no—
179Dic17—42no—
180Dic17—81no—
181Dic17—81no—
182Dic17—81no—
183Dic17—162no—
184C2×C4×Q8—171no—
185C2×C4×D4C2×D1711yescharacteristic
186C2×#99—341no—
187C2×C22⋊C8—21no—
188#399—171no—
189#399—171no—
190#393—171no—
191#393—171no—
192#390—341no—
193#389—341no—
194#385—341no—
195#385—341no—
196#382—171no—
197#380—341no—
198#342—172no—
199#324—21no—
200#323C2×D1712yes—
201C2×C17—21no—
202C2×C17—21no—
203C2×C17—41no—
204C2×C17—42no—
205C2×C17—41no—
206C2×C17#152011yescharacteristic
207C2×C17#212011yescharacteristic
208C2×C17#212711yescharacteristic
209C22×Q8—171no—
210C22×D4D6811yescharacteristic
211C23×C4D6811yescharacteristic
212C23×C4C22⋊D1711yescharacteristic
213C22×C8—41no—
214C4×Q8—681no—
215C4×Q8—681no—
216C4×D4—41no—
217C4×D4—41no—
218C2×C4⋊C4—171no—
219C2×C4⋊C4—341no—
220C2×C4⋊C4—341no—
221C2×C4⋊C4—341no—
222C2×C4⋊C4—341no—
223C2×C4⋊C4—681no—
224C2×C4⋊C4C22⋊D1711yescharacteristic
225C2×C22⋊C4—341no—
226C2×C22⋊C4—341no—
227C2×C22⋊C4—342no—
228C2×C22⋊C4—341no—
229C2×C22⋊C4—341no—
230C2×C22⋊C4C4×D1711yescharacteristic
231C2×C22⋊C4C22×D1711yescharacteristic
232C2×C42—341no—
233C2×C42C4×D1711yescharacteristic
234#99—682no—
235C22⋊C8—22no—
236C22⋊C8—41no—
237#95—171no—
238#95—171no—
239#95—341no—
240#95—341no—
241#95—341no—
242#95—681no—
243C17#1189711yescharacteristic, complemented, Sylow
244C24#6322711yescharacteristic
245C24C2×D6811yescharacteristic
246C2×Q8—681no—
247C2×Q8—682no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4#6321912yes—
251C2×D4Dic6812yes—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—81no—
257C22×C4—81no—
258C22×C4—341no—
259C22×C4—341no—
260C22×C4—341no—
261C22×C4—341no—
262C22×C4—682no—
263C22×C4#6322711yescharacteristic
264C22×C4#6322711yescharacteristic
265C22×C4#6322711yescharacteristic
266C22×C4C2×C4×D1711yescharacteristic
267C22×C4C2×C22⋊D1711yescharacteristic
268C2×C8—42no—
269C2×C8—82no—
270C4⋊C4—41no—
271C4⋊C4—681no—
272C4⋊C4—682no—
273C4⋊C4—681no—
274C4⋊C4—681no—
275C4⋊C4—1361no—
276C4⋊C4—1361no—
277C4⋊C4—1362no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C22⋊C4—682no—
281C22⋊C4—682no—
282C22⋊C4—682no—
283C22⋊C4—682no—
284C22⋊C4—1361no—
285C22⋊C4—1361no—
286C42—21no—
287C42—21no—
288C42—682no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23#1058748712yes—
298C23C2×#6321911yescharacteristic
299C23C2×Dic6811yescharacteristic
300C23C2×#6322711yescharacteristic
301Q8—682no—
302Q8—682no—
303D4—42no—
304D4—42no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—342no—
319C2×C4—681no—
320C2×C4—681no—
321C2×C4—681no—
322C2×C4—681no—
323C2×C4—681no—
324C2×C4—681no—
325C2×C4—681no—
326C2×C4—681no—
327C2×C4—681no—
328C2×C4—681no—
329C2×C4—681no—
330C2×C4—1362no—
331C2×C4—1362no—
332C2×C4—1362no—
333C2×C4#1058747711yescharacteristic
334C2×C4#1058747711yescharacteristic
335C2×C4#1058748712yes—
336C8—82no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—22no—
341C22—21no—
342C22—42no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—81no—
350C22—81no—
351C22C2×#1058747711yescharacteristic
352C22C2×#1058748711yescharacteristic
353C22#1176282511yescharacteristic
354C4—22no—
355C4—21no—
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—2722no—
361C4—682no—
362C4—1361no—
363C4—1361no—
364C4—1361no—
365C2—21no—
366C2—21no—
367C2—41no—
368C2—42no—
369C2—41no—
370C2#1452735711yescharacteristic
371C2#1453042611yescharacteristic
372C2#1453045111yescharacteristic
subgroupG/H
centerC22C2×#10587477
commutatorC22×C4×C17C22×C4
FrattiniC2×C22⋊C4C22×D17
FittingC17×#1459C2
socleC22×C17C2×#99
prime radicalC22×D4×C17D4
cosocleC2×C22⋊C4×C17C23
hypercenter#1459D17
hypocenterC17#11897
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1459

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #14526809C2semidirect
4. #14526806C2semidirect
6. C2×C4×Dic34C4semidirect
8. #11762745C4semidirect
10. #11762721C4semidirect
16. #11762675C4semidirect
243. C17#11897semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145341382
#145287722
#145268092
#145268062
C17×#14592
#1189717